Calculus, Gauge Theory and Noncommutative Worlds

This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, structure of Levi–Civita connection, and generalizations electromagnetism that related to theory with early work Hermann Weyl. The territory here explored is self-contained mathematically. It elementary, algebraic, subject possible discussed body paper.